1. Triangles
7.G.2 Focus on knowing the properties of triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

2. Is it a triangle? Triangle Angle Sum Theorem
This theorem states that the sum of the angles in any triangle is ALWAYS 180⁰.
Example:

3. Is it a triangle?
What is the measure of the missing angle? Justify your answer.

4. Triangle Inequality Theorem x + y > z x + z > y y + z > x
Is it a triangle?
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
x + y > z x + z > y y + z > x

5. Using the Triangle Inequality Theorem Are both examples triangles based under the theorem? Example 1: Example 2:

6. Find the measurement of the other side in order to meet the triangle inequality theorem.

7. Not a triangle!!!

8. Conditions for Triangles
Unique triangles, more than one triangle exist, or no triangle Unique – when 2 sides and an included angle are given it's known as unique. Ex. A unique triangle can be drawn with sides AB = 10 cm, BC = 11 cm and AC = 9 cm (with Angle A = 71°, Angle B = 50° and Angle C = 59°). In general, a unique triangle may always be drawn if three side lengths are given and the sum of any two is greater than the third. More than one triangle – If all angles add to 180 degrees, a triangle can have infinite amount of triangles if no sides are given. No triangle – When none of the above conditions of triangles are met, then no triangle exist.

9. Triangle or not? Justify........
#1. Do the lengths 4, 8, 11 make a triangle? #2 #4. #3. #5.